SOLUTION: In the diagram below, AC is the median of triangle ABD. Find the area of triangle ABD Diagram: https://imgur.com/a/vr9cZmy

Question 1149604: In the diagram below, AC is the median of triangle ABD. Find the area of triangle ABD
Diagram: https://imgur.com/a/vr9cZmy
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Given image

Let point E be the midpoint of segment BC. The red triangle AEC has unknown height h and unknown base x

Focusing solely on triangle AEC, we can use the pythagorean theorem to say

subtract x^2 from both sides

We'll use the last equation later on

---------------------
Mark triangle AED with another color. I'll use green. This triangle also has height h, but the base is now 3x

The 3x is from the fact that

EC = x
CD = BC = 2x
ED = EC+CD = x+2x = 3x

Once again, use the pythagorean theorem, but focus solely on triangle AED.

Replace with (we're using found earlier)

Subtract 289 from both sides

Divide both sides by 8

Apply square root to both sides

Multiply both sides by 4

The base of triangle ABD is exactly units long

---------------------

Use that info to find the following value for h

----------------------

Now compute the area of triangle ABD

Exact area

Approximate area

Units are in square cm, often written as

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